Net Change Theorem

The new value of a changing quantity is the initial value plus the integral of the rate of change:

F(𝒷) = F(𝒶) + ∫ 𝒶 𝒷 F′(x) dx

equivalently the net change from 𝒶 to 𝒷 is

F(𝒷) - F(𝒶) = ∫ 𝒶 𝒷 F′(x) dx

Examples

Velocity of a particle is 𝓋(t) = 𝓅′ (t) = 3⁢t-5 . Find:

  • net displacement from t=0 to t=3
  • total distance traveled from t=0 to t=3